Can You Solve This Fractional Exponent Equation?
Автор: Math Hacks Hub
Загружено: 2026-01-15
Просмотров: 95
Can you find x from this challenging equation?
Solve: x^(1/10) + x^(1/15) = 150, Find x
This problem combines tenth roots and fifteenth roots equaling 150, which looks incredibly difficult! But there's a powerful substitution technique using the LCM of the exponents. The key is recognizing that 1/10 and 1/15 have LCM = 1/30, so let y = x^(1/30). This transforms the equation into y³ + y² = 150, a much simpler polynomial equation.
💡 Pause and try solving it before watching!
This problem teaches you:
✓ Fractional exponent equations
✓ Strategic substitution methods
✓ LCM of exponents approach
✓ Polynomial transformation
✓ Working with multiple root types
Perfect for students preparing for:
• Math Olympiads IMO, AMC, AIME
• Competition mathematics
• Algebra II and Pre-Calculus courses
• Anyone who loves challenging algebra!
The solution requires clever substitution but yields a clean answer!
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